If I put a $2$ on one side and two $1$s on the other side, it is
balanced.
If I put a $3$ on one side, I would need three $1$s to make it
balance. How else could I make it balance with just a $3$ on one
side?

If I had a $3$ and a $4$ on one side and three $2$s on the other
side, what do I need to add to make it balance and where?

I hang a $10$ on one side. How many different ways can you find of
hanging numbers on the other side to make it balance?